Capacity and optimal power allocation for fading broadcast channels with minimum rates

We derive the capacity region and optimal power allocation scheme for a slowly fading broadcast channel in which minimum rates must be maintained for each user in all fading states, assuming perfect channel state information at the transmitter and at all receivers. We show that the minimum-rate capacity region can be written in terms of the ergodic capacity region of a broadcast channel with an effective noise determined by the minimum rate requirements. This allows us to characterize the optimal power allocation schemes for minimum-rate capacity in terms of the optimal power allocations schemes that maximize ergodic capacity of the broadcast channel with effective noise. Numerical results are provided for different fading broadcast channel models.     

Capacity Bounds for Broadcast Channels With Confidential Messages

This paper studies capacity bounds for discrete memoryless broadcast channels with confidential messages. Two private messages as well as a common message are transmitted; the common message is to be decoded by both receivers, while each private message is only for its intended receiver. In addition, each private message is to be kept secret from the unintended receiver where secrecy is measured by equivocation. Both inner and outer bounds are proposed to the rate equivocation region for broadcast channels with confidential messages. The proposed inner bound generalizes Csiszar and Korner's rate equivocation region for broadcast channels with a single confidential message, Liu 's achievable rate region for broadcast channels with perfect secrecy, Marton's and Gel'fand-Pinsker's achievable rate region for general broadcast channels. The proposed outer bounds, together with the inner bound, help establish the rate equivocation region of several classes of discrete memoryless broadcast channels with confidential messages, including the less noisy, deterministic, and semideterministic broadcast channels. Furthermore, specializing to the general broadcast channel by removing the confidentiality constraint, the proposed outer bounds reduce to new capacity outer bounds for the discrete memory broadcast channel.     

On the duality of Gaussian multiple-access and broadcast channels

We define a duality between Gaussian multiple-access channels (MACs) and Gaussian broadcast channels (BCs). The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of the BC (both constant and fading) can be written in terms of the capacity region of the dual MAC, and vice versa. We can use this result to find the capacity region of the MAC if the capacity region of only the BC is known, and vice versa. For fading channels we show duality under ergodic capacity, but duality also holds for different capacity definitions for fading channels such as outage capacity and minimum-rate capacity. Using duality, many results known for only one of the two channels can be extended to the dual channel as well.     

Capacity and optimal resource allocation for fading broadcastchannels .II. Outage capacity

For pt.I see ibid., vol.47, no.3, p.1083-1102 (2002). We study three capacity regions for fading broadcast channels and obtain their corresponding optimal resource allocation strategies: the ergodic (Shannon) capacity region, the zero-outage capacity region, and the capacity region with outage. In this paper, we derive the outage capacity regions of fading broadcast channels, assuming that both the transmitter and the receivers have perfect channel side information. These capacity regions and the associate optimal resource allocation policies are obtained for code division (CD) with and without successive decoding, for time division (TD), and for frequency division (FD). We show that in an M-user broadcast system, the outage capacity region is implicitly obtained by deriving the outage probability region for a given rate vector. Given the required rate of each user, we find a strategy which bounds the outage probability region for different spectrum-sharing techniques. The corresponding optimal power allocation scheme is a multiuser generalization of the threshold-decision rule for a single-user fading channel. Also discussed is a simpler minimum common outage probability problem under the assumption that the broadcast channel is either not used at all when fading is severe or used simultaneously for all users. Numerical results for the different outage capacity regions are obtained for the Nakagami-m (1960) fading model     

Capacity and optimal resource allocation for fading broadcastchannels .I. Ergodic capacity

In multiuser wireless systems, dynamic resource allocation between users and over time significantly improves efficiency and performance. In this two-part paper, we study three types of capacity regions for fading broadcast channels and obtain their corresponding optimal resource allocation strategies: the ergodic (Shannon) capacity region, the zero-outage capacity region, and the outage capacity region with nonzero outage. We derive the ergodic capacity region of an M-user fading broadcast channel for code division (CD), time division (TD), and frequency division (FD), assuming that both the transmitter and the receivers have perfect channel side information (CSI). It is shown that by allowing dynamic resource allocation, TD, FD, and CD without successive decoding have the same ergodic capacity region, while optimal CD has a larger region. Optimal resource allocation policies are obtained for these different spectrum-sharing techniques. A simple suboptimal policy is also proposed for TD and CD without successive decoding that results in a rate region quite close to the ergodic capacity region. Numerical results are provided for different fading broadcast channels     

Discrete Memoryless Interference and Broadcast Channels With Confidential Messages: Secrecy Rate Regions

We study information-theoretic security for discrete memoryless interference and broadcast channels with independent confidential messages sent to two receivers. Confidential messages are transmitted to their respective receivers while ensuring mutual information-theoretic secrecy. That is, each receiver is kept in total ignorance with respect to the message intended for the other receiver. The secrecy level is measured by the equivocation rate at the eavesdropping receiver. In this paper, we present inner and outer bounds on secrecy capacity regions for these two communication systems. The derived outer bounds have an identical mutual information expression that applies to both channel models. The difference is in the input distributions over which the expression is optimized. The inner bound rate regions are achieved by random binning techniques. For the broadcast channel, a double-binning coding scheme allows for both joint encoding and preserving of confidentiality. Furthermore, we show that, for a special case of the interference channel, referred to as the switch channel, derived bounds meet. Finally, we describe several transmission schemes for Gaussian interference channels and derive their achievable rate regions while ensuring mutual information-theoretic secrecy. An encoding scheme in which transmitters dedicate some of their power to create artificial noise is proposed and shown to outperform both time-sharing and simple multiplexed transmission of the confidential messages.     

Resource Allocation for Wireless Fading Relay Channels: Max-Min Solution

Resource allocation is investigated for fading relay channels under separate power constraints at the source and relay nodes. As a basic information-theoretic model for fading relay channels, the parallel relay channel is first studied, which consists of multiple independent three-terminal relay channels as subchannels. Lower and upper bounds on the capacity are derived, and are shown to match, and thus establish the capacity for the parallel relay channel with degraded subchannels. This capacity theorem is further demonstrated via the Gaussian parallel relay channel with degraded subchannels, for which the synchronized and asynchronized capacities are obtained. The capacity-achieving power allocation at the source and relay nodes among the subchannels is partially characterized for the synchronized case and fully characterized for the asynchronized case. The fading relay channel is then studied, which is based on the three-terminal relay channel with each communication link being corrupted by a multiplicative fading gain coefficient as well as an additive Gaussian noise term. For each link, the fading state information is assumed to be known at both the transmitter and the receiver. The source and relay nodes are allowed to allocate their power adaptively according to the instantaneous channel state information. The source and relay nodes are assumed to be subject to separate power constraints. For both the full-duplex and half-duplex cases, power allocations that maximize the achievable rates are obtained. In the half-duplex case, the power allocation needs to be jointly optimized with the channel resource (time and bandwidth) allocation between the two orthogonal channels over which the relay node transmits and receives. Capacities are established for fading relay channels that satisfy certain conditions.     

Secrecy Capacity Region of a Multiple-Antenna Gaussian Broadcast Channel With Confidential Messages

Wireless communication is particularly susceptible to eavesdropping due to its broadcast nature. Security and privacy systems have become critical for wireless providers and enterprise networks. This paper considers the problem of secret communication over the Gaussian broadcast channel, where a multiple-antenna transmitter wishes to send independent confidential messages to two users with information-theoretic secrecy. That is, each user would like to obtain its own confidential message in a reliable and safe manner. This communication model is referred to as the multiple-antenna Gaussian broadcast channel with confidential messages (MGBC-CM). Under this communication scenario, a secret dirty-paper coding scheme and the corresponding achievable secrecy rate region are first developed based on Gaussian codebooks. Next, a computable Sato-type outer bound on the secrecy capacity region is provided for the MGBC-CM. Furthermore, the Sato-type outer bound proves to be consistent with the boundary of the secret dirty-paper coding achievable rate region, and hence, the secrecy capacity region of the MGBC-CM is established. Finally, two numerical examples demonstrate that both users can achieve positive rates simultaneously under the information-theoretic secrecy requirement.      

Enhancing multicast security of cognitive radio networks with antenna correlations over Nakagami-m fading channels

In this paper, we investigate the impact of diversity and antenna correlations on the secrecy capacity and outage performance of a cognitive radio multicast network over Nakagami-m fading channels analytically. The proposed network consists of single primary and secondary user, multiple primary and secondary receivers, and multiple eavesdroppers. It is assumed that each user is equipped with single antenna while all the primary and secondary receivers, and eavesdroppers are equipped with multiple antennas. The primary and secondary users transmit their common messages to the respective receivers in the presence of multiple eavesdroppers. A mathematical model is developed to ensure successful reception of confidential information to the primary receivers protecting the activities of eavesdroppers neglecting the effect of interference due to secondary user. In order to analyze the security of the proposed model, closed-form analytical expressions have been derived for the secrecy multicast capacity, the secure outage probability for multicasting and the probability of non-zero secrecy multicast capacity. Analytical results are justified via Monte-Carlo simulations.

     

Secrecy outage probability of inter‐vehicular cognitive radio networks

Herein, we consider an underlay cognitive radio network (CRN) where mobile secondary user wishes to transmit a confidential information to the secondary destination in the presence of an illegitimate eavesdropper which is trying to steal the classified message signal. The proposed scenario can be viable for a secondary safety task force working with a primary regiment, which wishes to transmit the confidential information to the commander while an eavesdropper is trying to intercept the classified information. In the analysis, two novel power allocation methods are considered by assuming perfect and limited feedback channels of the primary network, and for both methods, exact and asymptotic expressions of secrecy outage probability (SOP) are derived for N*Nakagami‐m fading channels which are used to model fading channels such as mobile‐to‐mobile/vehicle‐to‐vehicle communication systems where the nodes are moving into a rich scattering environment. We further verified our analytic results through Monte‐Carlo simulations. It is shown from the numerical results that the cascading degree of the channels has a worsening effect on the secrecy outage performance of the CRN systems.     

Secure Broadcasting Over Fading Channels

We study a problem of broadcasting confidential messages to multiple receivers under an information-theoretic secrecy constraint. Two scenarios are considered: 1) all receivers are to obtain a common message; and 2) each receiver is to obtain an independent message. Moreover, two models are considered: parallel channels and fast-fading channels. For the case of reversely degraded parallel channels, one eavesdropper, and an arbitrary number of legitimate receivers, we determine the secrecy capacity for transmitting a common message, and the secrecy sum-capacity for transmitting independent messages. For the case of fast-fading channels, we assume that the channel state information of the legitimate receivers is known to all the terminals, while that of the eavesdropper is known only to itself. We show that, using a suitable binning strategy, a common message can be reliably and securely transmitted at a rate independent of the number of receivers. We also show that a simple opportunistic transmission strategy is optimal for the reliable and secure transmission of independent messages in the limit of large number of receivers.     

A broadcast approach for a single-user slowly fading MIMO channel

A broadcast transmission strategy for the slowly fading Gaussian multiple-input multiple-output (MIMO) channel is introduced. This broadcast strategy is an extension of the single-input single-output (SISO) broadcast approach. Perfect channel state information (CSI) is assumed known at the receiver end only. This strategy facilitates to adapt the reliably decoded rate to the actual channel state without having any feedback link to the transmitter. Transmission of layered coded information is motivated by the theory of majorization. We derive the basic equations characterizing achievable rates of the strategy. Several ad hoc approximations to the achievable region are considered and their performance is compared with the SISO setting and the ergodic capacity. It has been demonstrated that a single-layer outage approach is reasonably efficient in the MIMO setting in terms of the average reliably decoded rate. A multiple-access channel (MAC) broadcast approach is also applied for the MIMO case, and demonstrated to be relatively efficient.     

Capacity of Cognitive Interference Channels With and Without Secrecy

Like the conventional two-user interference channel, the cognitive interference channel consists of two transmitters whose signals interfere at two receivers. It is assumed that there is a common message (message 1) known to both transmitters, and an additional independent message (message 2) known only to the cognitive transmitter (transmitter 2). The cognitive receiver (receiver 2) needs to decode messages 1 and 2, while the noncognitive receiver (receiver 1) should decode only message 1. Furthermore, message 2 is assumed to be a confidential message which needs to be kept as secret as possible from receiver 1, which is viewed as an eavesdropper with regard to message 2. The level of secrecy is measured by the equivocation rate. In this paper, a single-letter expression for the capacity-equivocation region of the discrete memoryless cognitive interference channel is obtained. The capacity-equivocation region for the Gaussian cognitive interference channel is also obtained explicitly. Moreover, particularizing the capacity-equivocation region to the case without a secrecy constraint, the capacity region for the two-user cognitive interference channel is obtained, by providing a converse theorem.      

基于双变量泊松点过程的无线Ad Hoc网络的保密广播传输容量分析

本论文利用双变量泊松点过程对无线ad hoc广播网络和非法窃听网络共存的网络场景进行建模,运用随机几何工具,研究了无线ad hoc网络的保密广播传输容量,其定义为未发生窃听中断的广播发送节点密度、广播发送节点的相邻接收节点数量的平均值与保密速率的乘积.针对一般衰落和瑞利衰落信道条件,论文推导了造成保密中断的相邻窃听节点数量的平均值和保密广播传输容量的表达式.分析结果表明,与不存在相关性的网络场景相比,广播网络和窃听网络间的相关性会带来的保密广播传输容量的损失.     

具有功率分配因子的不可信中继系统的中断性能和遍历保密容量

基于不存在直接链路的具有不可信中继的三节点系统,本文在协作干扰模型中引入功率分配因子,对两种放大转发因子下系统的中断概率和遍历保密容量进行了计算及对比分析。首先,系统采用平均放大因子,推导出其保密中断概率;然后,在引入同样功率分配因子的基础上,系统改用自适应瞬时放大因子,得出保密中断概率的下界;为了对比,本文接着给出了系统两种情况下的遍历保密容量;最后,仿真验证了中断概率和遍历保密容量计算的准确性,数值仿真表明引入功率分配因子可减小系统的中断概率和提高系统的遍历保密容量,瞬时放大因子下系统性能较平均放大因子下更好。      

基于信道相关性的物理层安全性能分析

针对物理层安全研究中主窃信道具有相关性的场景,研究了主窃信道间的相关性对系统安全性能产生的影响,推导得到了遍历保密容量及中断概率的精确计算式,以及主窃信道的信道状态差异较大和较小这2种场景下的渐近计算式,并通过仿真验证了理论分析的正确性.研究结果表明,信道相关性会造成遍历保密容量的损失,但信道相关性强并不一定表明通信中...     

Secrecy Trade-off at the Physical Layer over Mixed Fading Multicast Channels Employing Antenna Diversity

This paper deals with the secrecy performance analysis of a multicast network over mixed fading scenarios in which a cluster of passive eavesdroppers is trying to overhear the secret transmission. Our key contribution is to prevent this malicious attack of the illegitimate receivers. Rayleigh/ Rician mixed fading channels are considered to model alternately the multicast/ eavesdropper and eavesdropper/ multicast channels as such mixed fading scenarios are often encountered in cellular communication where only one link (either multicast or eavesdropper) undergo a line-of-sight propagation path. At first, we derive the probability density functions for the single-input-multiple-output multicast scenarios and then the secrecy analysis is carried out by obtaining closed-form expressions for the performance matrices such as the probability of non-zero secrecy multicast capacity, ergodic secrecy multicast capacity, and secure outage probability for multicasting. The derived expressions are beneficial to investigate how the antenna diversity can combat the detrimental impact of fading as well as the number of multicast users and eavesdroppers, and improve the secrecy level to the acceptable limit. Moreover, the best secure scenario in terms of the secrecy parameters is obtained when the multicast channels undergo Rician fading whereas the eavesdropper channels experience Rayleigh fading. Finally, the analytical expressions are justified via the Monte-Carlo simulations.

     

Rate Regions for Relay Broadcast Channels

A partially cooperative relay broadcast channel (RBC) is a three-node network with one source node and two destination nodes (destinations 1 and 2) where destination 1 can act as a relay to assist destination 2. Inner and outer bounds on the capacity region of the discrete memoryless partially cooperative RBC are obtained. When the relay function is disabled, the inner bound reduces to an inner bound on the capacity region of broadcast channels that includes an inner bound of Marton, and GePfand and Pinsker. The outer bound reduces to a new outer bound on the capacity region of broadcast channels that generalizes an outer bound of Marton to include a common message, and that generalizes an outer bound of GePfand and Pinsker to apply to general discrete memoryless broadcast channels. The proof for the outer bound simplifies the proof of GePfand and Pinsker that was based on a recursive approach. Four classes of RBCs are studied in detail. For the partially cooperative RBC with degraded message sets, inner and outer bounds are obtained. For the semideterministic partially cooperative RBC and the orthogonal partially cooperative RBC, the capacity regions are established. For the parallel partially cooperative RBC with unmatched degraded subchannels, the capacity region is established for the case of degraded message sets. The capacity is also established when the source node has only a private message for destination 2, i.e., the channel reduces to a parallel relay channel with unmatched degraded subchannels.     

Service outage based power and rate allocation for parallel fading channels

The service outage based allocation problem explores variable-rate transmission schemes and combines the concepts of ergodic capacity and outage capacity for fading channels. A service outage occurs when the transmission rate is below a given basic rate r/sub o/. The allocation problem is to maximize the expected rate subject to the average power constraint and the constraint that the outage probability is less than /spl epsi/. A general class of probabilistic power allocation schemes is considered for an M-parallel fading channel model. The optimum power allocation scheme is derived and shown to be deterministic except at channel states of a boundary set. The resulting service outage achievable rate ranges from 1-/spl epsi/ of the outage capacity up to the ergodic capacity with increasing average power. Two near-optimum schemes are also derived by exploiting the fact that the outage probability is usually small. The second near-optimum scheme significantly reduces the computational complexity of the optimum solution; moreover, it has a simple structure for the implementation of transmission of mixed real-time and non-real-time services.     

Suboptimality of TDMA in the low-power regime

We consider multiaccess, broadcast, and interference channels with additive Gaussian noise. Although the set of rate pairs achievable by time-division multiple access (TDMA) is not equal to the capacity region, the TDMA achievable region converges to the capacity region as the power decreases. Furthermore, TDMA achieves the optimum minimum energy per bit. Despite those features, this paper shows that the growth of TDMA-achievable rates with the energy per bit is suboptimal in the low-power regime except in special cases: multiaccess channels where the users' energy per bit are identical and broadcast channels where the receivers have identical signal-to-noise ratios. For the additive Gaussian noise interference channel, we identify a small region of interference parameters outside of which TDMA is also shown to be suboptimal. The effect of fading (known to the receiver) on the suboptimality of TDMA is also explored.